Pseudo Force

Q. A block of mass m is placed over a plank B of mass 2m. Plank B is placed over a smooth horizontal surface.The coefficient of friction between A and B is μ=0.5.Block A is given a velocity v_†extdegree towards right. Acceleration of B relative to A is (a)g/2 (b)g (c)3g/2 (d)zero ?

Q. A block is released from point $\text{A}$ as shown in figure. All surfaces are smooth and there is no loss of mechanical energy anywhere. Find the time period of oscillations of block.

1. $2\sqrt{\frac{2h}{g}}[\frac{1}{\sin \alpha }+\frac{1}{\sin \beta }]$
2. $2\sqrt{\frac{2h}{g}}[\sin \alpha +\cos \beta ]$
3. $2\sqrt{\frac{h}{g}}[\frac{1}{\sin \alpha }+\frac{1}{\sin \beta }]$
4. $2\sqrt{\frac{2h}{g}}[\frac{1}{\sin \alpha }+\sin \beta ]$

Q. If acceleration of A is 2 m/s2 which is smaller thanacceleration of B then the value of frictional forceapplied by B on A is

Q. A block of mass m is pulled by a constant power P placed on a rough horizontal plane.The friction coefficient between the block and surface varies with its speed v as μ=\sqrt{1+v}.The acceleration of the block when the speed is 3ms-1willbe

Q.

Which of the following is a necessary and sufficient condition for S.H.M.

[NCERT 1974]

1. Constant period

2. Constant acceleration

3. Proportionality between acceleration and displacement from equilibrium position

4. Proportionality between restoring force and displacement from equilibrium position

Q. 50.Acceleration of block A varies with time as shown in figure the value of coefficient of kinetic friction between block A and B is

Q. four thin rod each of mass m and length l are joined to make a square find the momentem of interia af all. the four rods about any side a square

Q.

Is Spring force a restoring force?

Q. A downward force of $100\text{N}$ is applied to the small piston with a diameter of $50\text{cm}$ in the hydraulic lift system as shown in figure. What will be the upward force exerted on the large position with a diameter of $1\text{m}$?

1. $300\text{N}$
2. $50\text{N}$
3. $400\text{N}$
4. $600\text{N}$

Q. A block of mass $m$ is kept on a wedge of mass $M$. Initially the system is held. At certain time the system is released and the wedge is observed to move with acceleration $A$ on inclined surface as shown. There is no friction anywhere. The acceleration of block $\left(m\right)$ with respect to wedge $\left(M\right)$ will be

1. $A$ rightward
2. $A\cos \theta$ rightward
3. $A\cos \theta$ leftward
4. none of these

Q. The apparent weight of a person in an elevator is less than the weight of the person if the lift is

1. moving with a constant velocity
2. moving with a constant acceleration
3. accelerating downwards
4. accelerating upwards

Q. A moving body with mass m1 strike a stationary body of mass m2 . The masses m1 and m2 should be in the ratio m1/m2 so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact . then the ratio m1/m2 is

Q. a uniform chain has mass M and lengthL it is placed on a frictionless table with length L_0 hanging over the edge the chain begaing to slide own then the speed v with which the end slides down the edge is given by a)\sqrt{g/L(L+l_0)} b)\sqrt[{}]{g/L(L-l_0)} c)\sqrt{g/L(L^2-l_0^2)} d)\sqrt{2g(L-l_0)

Q. in two systems of relations among velocity , accleration anf force are respectively v_2 = α_{2/β}v_1, a_2=αβ a_1 and F_2=F_{1/αβ.} if α and β are cons†an ts then relations among mass, length and time in two systems are

Q. Consider a special situtation in which both the faces of the block $M_0$ are smooth, as shown in adjoining figure. Mark out the correct statement(s)


(A) If $F=0$, the blocks $M$ and $m$ cannot remain stationary
(B) For one unique value of $F$, the blocks $M$ and $m$ remain stationary with respect to block $M_0$
(C) There exists a range of $F$ for which blocks $M$ and $m$ remain stationary with respect to block $M_0$
(D) Since there is no friction, therefore, blocks $M$ and $m$ cannot be in equillibrium with respect to block $M_0$

1. $\text{Only Statement A is Correct}$
2. $\text{Only Statement B is Correct}$
3. $\text{Only Statement C is Correct}$
4. $\text{Both Statement A and B are Correct}$

Q. A small block on a rough inclined plane inclined at an angle of 30 degree with the horizontal slides down the plane with certain acceleration. when the inclination of the plane is increased to 60 degree, the acceleration is found doubled. the coefficient of friction between the plane and the block is nearly. (1)0.11 (2)0.55 (3)0.65 (4)0.41

Q. .rod of length l is pivoted at one of the ends andis made to rotate in a horizontal plane as shown infigure with a constant angular speed. A ball of massm suspended by a string of length from the otherend of the rod. If the angle made by the string withthe vertical is x then angular speed of rotation is:-

Q. A long plank begins to move at t = 0 and accelerates with a speed given by v = (2t^2 + 2) m/s^{-1}. A small block initially at rest on the plank begins to slip at t is equal to (Coefficient of friction between block and plank has μ_s= 0.4 and μ_k = 0.3) (Take g = 10 m/s^2)

Q. 85.Two mass are connected by a string which passes over a pulley accelerating upwards at a rate A as shown. If a1 and a2 be the acceleration of bodies 1 and 2 respectively then

Q. The elevator shown in the figure is descending with an acceleration of $2m/s^2$. The mass of the block $A=0.5\text{kg}$. The force exerted by the block $A$ on the block $B$ is (take $g=10{\text{m/s}}^2$)

1. $2\text{N}$
2. $4\text{N}$
3. $6\text{N}$
4. $8\text{N}$

Q. A uniform rod PQ of mass m and length l rotates with an angular vel. ω while its centre moves with linear vel. v=2ω l/3 on a smooth horizontal surface. If the end Q of the rod is suddenly gets stuck at the moment , then angular vel. of the rod will be ( ω is in anticlockwise direction about the centr of the rod and its P end is downwards and Q end upwards)-

Q. A vehicle is moving on a road with an acceleration a=20 .the frictional coefficient between the block of mass m and the vehicle so that block is does not fall downward

Q.

Q. If a stone is thrown out of an accelerated train, then acceleration of the stone at any instant depends on

1. force acting on it at that instant.
2. acceleration of the train.
3. Both (a) and (b)
4. None of these

Q. A constant retarding force of $50$ $N$ is applied to a body of mass $20$ $kg$ moving initially with a speed of $15$ $m{s}^{-1}$. How long does the body take to stop?

Q. a lorry starting from rest moving with acceleration 2m/s2 has a trolley 4.5m long. a box is placed at 4.5 m from the open end and coefficient of friction between box and lorry is 0.02. the distance covered by the lorry by the time the box falls off the trolley is (g=10 m/s 2).

Q. In the figure the reading of the spring balance will be $:[g=10\frac{m}{s^2}]$

1. $50N$
2. $40N$
3. $60N$
4. $70N$

Q.

.A uniform rod of mass m and length l is hanging with the help of two strings as shown in the figure-

If T₁ and T₂ be tensions in the strings, then-

1. $T_1>T_2$

2. $T_1<T_2$

3. $T_1+T_2=mg$

4. $T_1=T_2$

Q. A package is kept on a conveyor belt and the system is at rest. The belt starts to move to the right for $1.3\text{s}$ with a constant acceleration of $2{\text{m/s}}^2$. The belt then moves with constant deceleration $a{\text{m/s}}^2$ and comes to a stop after a total displacement of $2.2\text{m}$. Knowing that the coefficient of static friction between the package and the belt is $0.35$ and coefficient of kinetic friction is $0.25$. Then determine the displacement of the package relative to the belt as the belt comes to stop. Take $g=10{\text{m/s}}^2$.

1. $0.33\text{m}$
2. $0.66\text{m}$
3. $0.22\text{m}$
4. $0.11\text{m}$

Q.

With what acceleration 'a' should the lift descend so that the block of mass M exerts a force $\frac{Mg}{4}$ on the floor of the box?

1. 2g

2. 

3. 

4. g